Polya's "How to Solve It"

Main Questions

1. What is the unknown?
2. What are the data?
3. What is the condition [constraint]?

Problem Solving Phases

1. Understand the problem.
2. Make a plan.
3. Carry out the plan.
4. Review and discuss the completed solution.

Techniques

• Try to think of a familiar problem having the same or similar unknown.
• Imitate and practice.
• Draw a figure.
• Introduce suitable notation.
• If you cannot solve the proposed problem, first solve a related or simpler one, e.g. by dropping some constraints or dealing with a subset of the data.
• Did you use all the data and conditions? If not, is there something wrong?
• Can you see clearly that a given step is correct? Better, can you prove it?
• Can you check the result by deriving it differently?
• Try restating the problem.
• Try working backward from the unknown toward the data.